Tsinghua Researchers Use GPT to Solve 40-Year-Old Optimization Problem
新智元 · wechat · 2026-08-23
Researchers from Tsinghua University and Wharton used GPT-5.6SolPro to solve a 40-year-old problem in optimization theory: gradient descent cannot achieve O(1/T²) convergence by tuning step sizes alone.
Key Breakthroughs:
- AI-Driven Proof: Using a "resisting oracle" strategy, GPT-5.6 constructed a complex geometric proof establishing the upper bound of convergence for pure step-size tuning as Ω(T^{-1.9319}).
- Lean4 Formal Verification: The proof was transcribed to Lean4 code via Codex and verified line-by-line by the compiler, achieving "zero sorry, zero admit".
- Conclusion: Achieving Nesterov acceleration requires altering the algorithm structure, not just adjusting step sizes.
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